The following table shows the amount of air leaking from an inflatable as a function of time:

time (in minutes)
x air (in ounces)
f(x)
0 64
1 56
2 48
3 40
4 32

find and interpret the meaning of the x-intercept in this scenario.
a (8, 0); the time it takes all the air to leave the inflatable
b (64, 0); the time it takes all the air to leave the inflatable
c (64, 0); the time it takes to fill up inflatable with air
d (8, 0); the time it takes to fill up inflatable with air

Option a.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

Where "m" is the slope and "b" is the y-intercept.

Find the slope of the line with this formula:

Choose two points from the table and substitute the coordinates into the formula. Then, the slope is:

 By definition, the line intersects the y-axis when the value of "x" is zero.  So, based on the table, the y-intercept is:

Then the equation of the line is:

The line intersects the x-axis when the value of "y" is zero, then  substituting y=0 into the equation of this line, and solving for "x", you get:

So, the point of intersection with the x-axis is:

Since the table shows the amount of air leaking from an inflatable as a function of time, you can conclude that meaning of the x-intercept in this scenario is: "The time it takes all the air to leave the inflatable".

a

step-by-step explanation:

it has the same slope and a different y-intercept

hope this : )